Statistics and Probability Answers

In testing a certain kind of truck tire over a rugged

terrain, it is found that 25% of the trucks fail to

complete the test run without a blowout. Of the next

15 trucks tested, find the probability that a) From 3

to 6 have blowouts; b) Fewer than 4 have blowouts;

C) More than 5 have blowouts.

If a given score is at the 30th percentile for reference group A and the same score is at the 60th percentile for reference group B, how do the two groups compare in terms of performance

An experiment has a binary outcome. Either success or failure. The probability of success is always 0.15. Suppose that the experiment is repeated 30 times.

a. Find out the probability that there are exactly 10 successes. 

b. Calculate the same probability using a Normal Approximation. Is the approximation good? If so why? If not why not?

A supervisor at an electric bulb factory examines bulbs produced in the factory for defects. She usually finds that there are 14 defective bulbs in a week (7 days).

a. What is the probability that there are exactly 3 defective bulbs in one day?

b. What is the probability that there are less than 5 defects in a day?

c. Suppose the supervisor joins work, find the probability that 72 hours go by before she discovers her first defective bulb.

According to IT department of leading financial firm, 50% of emails received by their employees are spam. They are planning to install a software which filters the spam emails. A reputable cybersecurity brand has launched a software which claims to detect 99% of spam emails. However, they have also reported 5% as the chance of detecting a nonspam email as spam. If an email is detected as spam, what is the probability of it in fact being a non-spam email? 

Rohini has 3 scarfs which are identical in shape, form and cloth material. They are only different in colours. The first scarf is coloured red on both sides while both the sides of second scarf are coloured black. The third scarf is coloured black on one side and red on the other. She mixes the 3 scarfs in a box and randomly selects one scarfs and puts it down on the ground. If the upper side of the selected scarf is red in colour, what is the probability of the other side of the scarf to be black?

JGU students recently conducted a study to record the height of Asian Females in Haryana. They found the heights to be normally distributed with a mean 66 inches and a standard deviation of 2.5 inches.

a. Suppose a female is randomly selected. What is the probability of her height being between 65 and 69 inches.

b. Is it possible to meet a female in Haryana with a height more than 72 inches?

In 2016, around 12 Lakh students gave the CAT to bag an admission in India’s best business schools. In the math section of CAT, the marks follow a normal distribution with mean 520 and standard deviation 115.

A. What CAT score will be 1.5 standard deviations above the mean?

b. In 2022, a significant number of students also gave GMAT. Some colleges in India also accept GMAT scores as an alternative to CAT. The math section of GMAT is normally distributed with mean 21 and standard deviation 5.3. The math section is CAT-2022 also follows a normal distribution with mean 514 and standard deviation of 117. Raj took the CAT and scored 700 in the math section. Meanwhile, his friend Rahul scored 30 in the GMAT math section. Who do you think performed better? 

Find 80%, 85%, 99, 99% confidence interval for the sample mean of a population,. if we know that a random sample of 70. people from the population, the sample mean is 60 and standard deviation. is. 5

The mean dying rate of mice administered yo a given dosage of an experimental drug is 45with a variance of 25. What is the probability randomly selected 55 mice, which received the drug, more than 50 will die? Assume normality